Properties of Stark Resonant States in Exactly Solvable Systems

Properties of Stark Resonant States in Exactly Solvable Systems

Properties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions. Analytic expressions are derived for the pseud...

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Main Authors: Jeffrey M. Brown, Miroslav Kolesik
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2015/125832
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spelling doaj-d5fce4d78b2147c19f1db138e5e5a8a92021-07-02T01:58:23ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/125832125832Properties of Stark Resonant States in Exactly Solvable SystemsJeffrey M. Brown0Miroslav Kolesik1College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USACollege of Optical Sciences, University of Arizona, Tucson, AZ 85721, USAProperties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions. Analytic expressions are derived for the pseudonorm, dipole moment, and coupling matrix elements which relate systems with different strengths of the external field. All results are based on explicit calculations made possible by a newly designed integration method for combinations of Airy functions representing resonant eigenstates. Generalizations for one-dimensional systems with short-range potentials are presented, and relations are identified which are likely to hold in systems with three spatial dimensions.http://dx.doi.org/10.1155/2015/125832
collection DOAJ
language English
format Article
sources DOAJ
author Jeffrey M. Brown
Miroslav Kolesik
spellingShingle Jeffrey M. Brown
Miroslav Kolesik
Properties of Stark Resonant States in Exactly Solvable Systems
Advances in Mathematical Physics
author_facet Jeffrey M. Brown
Miroslav Kolesik
author_sort Jeffrey M. Brown
title Properties of Stark Resonant States in Exactly Solvable Systems
title_short Properties of Stark Resonant States in Exactly Solvable Systems
title_full Properties of Stark Resonant States in Exactly Solvable Systems
title_fullStr Properties of Stark Resonant States in Exactly Solvable Systems
title_full_unstemmed Properties of Stark Resonant States in Exactly Solvable Systems
title_sort properties of stark resonant states in exactly solvable systems
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2015-01-01
description Properties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions. Analytic expressions are derived for the pseudonorm, dipole moment, and coupling matrix elements which relate systems with different strengths of the external field. All results are based on explicit calculations made possible by a newly designed integration method for combinations of Airy functions representing resonant eigenstates. Generalizations for one-dimensional systems with short-range potentials are presented, and relations are identified which are likely to hold in systems with three spatial dimensions.
url http://dx.doi.org/10.1155/2015/125832
work_keys_str_mv AT jeffreymbrown propertiesofstarkresonantstatesinexactlysolvablesystems
AT miroslavkolesik propertiesofstarkresonantstatesinexactlysolvablesystems
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